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Öğe Discussion on $(k, s)$-Riemann Liouville fractional integral and applications(Hacettepe Üniversitesi, 2024) Benaissa, Bouharket; Sarıkaya, Mehmet ZekiIn this paper we present the correct version of Theorem 2.2 in [$(k; s)$-Riemann-Liouville fractional integral and applications, Hacet. J. Math. Stat. \textbf{45} (1), 77 - 89, 2016] and prove it.Öğe General (k, p)-Riemann-Liouville fractional integrals(Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Budak, HüseyinThe main motivation of this study is to establish a general version of the Riemann-Liouville fractional integrals with two exponential parameters k and p which is determined over the (k, p)-gamma function. In particular, we present the harmonic, geometric and arithmetic (k, p)- Riemann-Liouville fractional integrals. When p = k, these integrals reduce to k-Riemann-Liouville fractional integrals. Some formulas relating to general (k, p)-Riemann-Liouville fraction integrals are also given.Öğe A GENERALIZATION OF WEIGHTED BILINEAR HARDY INEQUALITY(Publishing House of the Romanian Academy, 2021) Benaissa, Bouharket; Zeki Sarıkaya, MehmetIn this paper, we give some new generalizations of the weighted bilinear Hardy inequality by using weighted mean operators S:= (Sf)w g, where f nonnegative integrable function with two variables on ? = (0,+?)×(0,+?), defined by with where w is a weight function and g is a nonnegative continuous function on (0,+?). © 2021, Publishing House of the Romanian Academy. All rights reserved.Öğe Hermite-Hadamard type inequalities for new conditions on h-convex functions via ? -Hilfer integral operators(Springer Basel Ag, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, HüseyinWe employ a new function class called B-function to create a new version of fractional Hermite-Hadamard and trapezoid type inequalities on the right-hand side that involves h-convex and psi -Hilfer operators. We also provide new midpoint-type inequalities using h-convex functions.Öğe MORE ON REVERSE OF HOLDER'S INTEGRAL INEQUALITY(Kangwon-Kyungki Mathematical Soc, 2020) Benaissa, Bouharket; Budak, HüseyinIn 2012, Sulaiman [7] proved integral inequalities concerning reverse of Holder's. In this paper two results are given. First one is further improvement of the reverse Holder inequality. We note that many existing inequalities related to the Holder inequality can be proved via obtained this inequality in here. The second is further generalization of Sulaiman's integral inequalities concerning reverses of Holder's [7].Öğe On some Grüss-type inequalities via k-weighted fractional operators(Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Sarıkaya, Mehmet ZekiIn this paper, we employ the concept of k-weighted fractional integration of one function with respect to another function to extend the scope of Gr & uuml;ss-type fractional integral inequalities. Furthermore, we establish and provide proofs for a set of inequalities that incorporate k-weighted fractional integrals.Öğe On some new Hardy-type inequalities(Wiley, 2020) Benaissa, Bouharket; Sarıkaya, Mehmet Zeki; Senouci, AbdelkaderIn this paper, we give some new types of the classical Hardy integral inequality by including a second parameter q and using weighted mean operators S-1 := (S-1)(g)(w) and S-2 := (S-2)(g)(w) defined by S-1(x) = 1/W(x) integral(x)(a) w(t)g(f(t))dt, S-2(x) = integral(x)(a) w(t)/W(t)g(f(t))dt, with W(x) = integral(x)(0) w(t)dt, for x is an element of(0,+infinity), where w is a weight function and g is a real continuous function on (0,+infinity).Öğe On the refinements of some important inequalities with a finite set of positive numbers(Wiley, 2024) Benaissa, Bouharket; Sarıkaya, Mehmet ZekiIn this research, a novel method for enhancing the Holder-Iscan inequality through the utilization of both integrals and sums, as well as the mean power inequality, has been introduced. This approach outperforms traditional Holder and mean power integral inequalities by employing a finite set of functions. Through the careful selection of the function phi$$ \phi $$, an entirely new category of classical inequalities emerges for both Holder and mean power inequalities.Öğe Some Hardy-type integral inequalities involving functions of two independent variables(Springer, 2021) Benaissa, Bouharket; Sarıkaya, Mehmet ZekiIn this paper, we give some new generalizations to the Hardy-type integral inequalities for functions of two variables by using weighted mean operatorsS(1) := S1(w) f and S-2 := S-2(w) f defined by S-1(x, y) = 1/W(x)W(y) integral(x)(x/2) integral(y)(y/2) w(t)w(s) f (t, s)dsdt, and S-2(x, y) = integral(x)(x/2) integral(y)(y/2) w(t)w(s)/W(t)W(s) f (t, s)dsdt, with W (z) = integral(z)(0) w(r)dr f or z is an element of (0,+infinity), where w is a weight function.Öğe Weighted fractional inequalities for new conditions on h-convex functions(Springer, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, HüseyinWe use a new function class called B-function to establish a novel version of Hermite-Hadamard inequality for weighted psi-Hilfer operators. Additionally, we prove two new identities involving weighted psi-Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the B-function, we derive several trapezoid- and midpoint-type inequalities for h-convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function h.
